The following computer-generated description may contain errors and does not represent the quality of the book:The Differential and the Integral Calculus have been established upon entirely different axioms and definitions by the several founders of those sciences. The primary ideas of infinitesimals, fluxions, and exhaustions, though their results coincide, for the simple reason that all pure truth is consistent with itself, are widely diverse in their abstract nature. In writing, therefore, on the principles of either Calculus, a difficulty presents itself in the necessity of electing between systems, each of which has the sanction of high authority and peculiar intrinsic merits.

This consideration is of especial importance in a "Rudimentary Treatise," which cannot, of course, fulfil the profession of its title without singleness and simplicity of its fundamental ideas, and an exactness of thought and language often very difficult of attainment. The choice of methods in the present work has been determined partly by historical considerations. The discoverers of new truths usually search after them by the simplest and most familiar considerations; and it seems natural to presume that, as far at least as abstract principles are concerned, the way of discovery as the easiest way of instruction.